Abstract
Let {P_{n}}_{nge 0} be the sequence of Padovan numbers defined by P_0=0 , P_1 =1=P_2, and P_{n+3}= P_{n+1} +P_n for all nge 0 . In this paper, we find all repdigits in base 10 which can be written as a sum of three Padovan numbers.
Highlights
Let {Pn}n≥0 be the sequence of Padovan numbers given by P0 = 0, P1 = 1, P2 = 1, and Pn+3 = Pn+1 + Pn for all n ≥ 0
A repdigit is a positive integer N that has only one distinct digit when written in base 10
We study the problem of writing repdigits as sums of three Padovan numbers
Summary
Let {Pn}n≥0 be the sequence of Padovan numbers given by P0 = 0, P1 = 1, P2 = 1, and Pn+3 = Pn+1 + Pn for all n ≥ 0. This is sequence A000931 on the On-Line Encyclopedia of Integer Sequences (OEIS) [12]. The first few terms of this sequence are. A repdigit is a positive integer N that has only one distinct digit when written in base 10. For some positive integers d and with 1 ≤ d ≤ 9 and ≥ 2. The sequence of repdigits is sequence A010785 on the OEIS
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